• 대한수학회보
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• 제53권2호
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• 대한수학회논문집
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• 제34권2호
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• pp.585-602
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• 2019

We characterize Gelfand-continuous functions from a Tychonoff space X into an Arens-Michael algebra A. Then we define several algebras of such functions, and investigate them as topological algebras. Finally, we provide a class of examples of (metrizable) commutative unital complete Arens-Michael algebras A and locally compact spaces X for which all these algebras differ from each other.

• 대한수학회논문집
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• 제37권4호
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• pp.1041-1053
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• 2022

In this paper, sharp lower and upper bounds on the third order Hermitian-Toeplitz determinant for the classes of Sakaguchi functions and some of its subclasses related to right-half of lemniscate of Bernoulli, reverse lemniscate of Bernoulli and exponential functions are investigated.

• 호남수학학술지
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• 제45권1호
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• pp.71-81
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• 2023

In this paper, we deal with some geometric properties including starlikeness and convexity of order 𝛽 of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire functions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.

• 대한수학회보
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• 제60권2호
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권1호
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• pp.51-57
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• 2022

The Jensen, Simic and Mercer inequalities are very important inequalities in theory of inequalities and some results are devoted to this inequalities. In this paper, firstly, we establish extension of Jensen-Simic-Mercer inequality. After that, we investigate bounds for Shannons entropy of a probability distribution. Finally, We give some new applications in analysis.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2016년도 추계학술대회
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• pp.197-199
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• 2016

최근 약 10년 동안, 인지무선환경에서 1차사용자와 2차사용자간의 스펙트럼 공유를 시장 (market) 논리와 접목시키는 연구들이 활발하게 진행되어 왔다. 즉, 1차사용자가 자신이 소유하고 있는 주파수 자원을 2차사용자에게 금전적 보상을 받고 대여하는 형태를 고려하는 것이다. 그리고, 이에 대한 시장의 평형 (market equilibrium)을 이론적으로 제시하는 것이 그 연구들의 주요 목표이다. 우리는 이 논문에서, 1차사용자들은 2차사용자들에게 자신들의 유휴 채널의 사용권을 대여 또는 판매하는데, 1차사용자들은 허용가능한 간섭의 양을 정해놓고, 2차사용자가 그 간섭의 양을 초과하게 되면 금전적인 보상을 받는 시장 모델을 고려한다. 그리고, 각 2차사용자는 자신들이 1차사용자들에게 지급할 수 있는 예산에는 제한이 있는 상황도 추가 고려한다. 2차사용자의 재화는 자유공간상에서 획득 가능한 전송률이고 1차사용자의 재화는 금전적인 순이득 (net profit)이다. 우리는 이러한 인지무선네트워크 시장을 확장된 Fischer 마켓으로 모델링하고, Eisenberg-Gale convex program을 통해 마켓 균형을 찾는 방법을 제안한다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.433-437
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• 2003

Quantitative Feedback Theory (QFT) is one of effective methods of robust controller design. In QFT design we can considers the phase information of the perturbed plant so it is less conservative than $H_{\infty}$ and ${\mu}$-synthesis methods and as be shown, it is more transparent than the sensitivity reduction methods mentioned . In this paper we want to overcome the major drawback of QFT method which is lack of an automatic method for loop-shaping step of the method so we focus on the following problem: Given a nominal plant and QFT bounds, synthesize a controller that achieves closed-loop stability and satisfies the QFT boundaries. The usual approach to this problem involves loop-shaping in the frequency domain by manipulating the poles and zeros of the nominal loop transfer function. This process now aided by recently developed computer aided design tools proceeds by trial and error and its success often depends heavily on the experience of the loop-shaper. Thus for the novice and First time QFT user, there is a genuine need for an automatic loop-shaping tool to generate a first-cut solution. Clearly such an automatic process must involve some sort of optimization, and while recent results on convex optimization have found fruitful applications in other areas of control theory we have tried to use LMI theory for automating the loop-shaping step of QFT design.

• Journal of Electrical Engineering and Technology
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• 제10권5호
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• pp.1940-1949
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• 2015

This paper presents an Enhanced Particle Swarm Optimization (EPSO) to solve short-term hydrothermal scheduling (STHS) problem with non-convex fuel cost function and a variety of operational constraints related to hydro and thermal units. The operators of the conventional PSO are dynamically controlled using exponential functions for better exploration and exploitation of the search space. The overall methodology efficiently regulates the velocity of particles during their flight and results in substantial improvement in the conventional PSO. The effectiveness of the proposed method has been tested for STHS of two standard test generating systems while considering several operational constraints like system power balance constraints, power generation limit constraints, reservoir storage volume limit constraints, water discharge rate limit constraints, water dynamic balance constraints, initial and end reservoir storage volume limit constraints, valve-point loading effect, etc. The application results show that the proposed EPSO method is capable to solve the hard combinatorial constraint optimization problems very efficiently.

• 대한기계학회논문집A
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• 제25권3호
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• pp.369-380
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• 2001

Although extensive efforts have been devoted to the optimal design of composite laminated plates in recent years, some practical issues still need further research. Two of them are: the handling of the ply angle as either continuous or discrete; and that of the uncertainties in material properties, which were treated as continuous and ignored respectively in most researches in the past. In this paper, an algorithm for stacking sequence optimization which deals with discrete ply angles and that for thickness optimization which considers uncertainties in material properties are used for a two step optimization of composite laminated plates. In the stacking sequence optimization, the branch and bound method is modified to handle discrete variables; and in the thickness optimization, the convex modeling is used in calculating the failure criterion, given as constraint, to consider the uncertain material properties. Numerical results show that the optimal stacking sequence is found with fewer evaluations of objective function than expected with the size of feasible region taken into consideration; and the optimal thickness increases when the uncertainties of elastic moduli considered, which shows such uncertainties should not be ignored for safe and reliable designs.